theorem Th54:
  arccot|[.-1,1.] is continuous
proof
  set f = cot | [.PI/4,3/4*PI.];
  PI/4 < (PI/4)*3 by XREAL_1:155;
  then
A1: (f|[.PI/4,3/4*PI.])"|(f.:[.PI/4,3/4*PI.]) is continuous by Lm12,Lm14,
FCONT_1:47;
  f|[.PI/4,3/4*PI.] = f by RELAT_1:72;
  then arccot | [.-1,1.]|[.-1,1.] is continuous by A1,Th22,Th26,RELAT_1:115;
  hence thesis by FCONT_1:15;
end;
